从二次三项式的因式分解谈起

学习了多项式的因式分解后,同学们都知道,许多二次三项式都可用十字相乘法或配方法与公式法分解因式．例1分解因式：X’－6X－616解1用十字相乘法．因为一28x22＝－616,且一28＋22＝－6,所以原式一（。＋22）（x－28）．解2用配方法与公式法．原式二x‘－6。＋9－616－9＝（X’－6X＋9）－625＝＝（x－3）‘－252二（x、3＋25）（x、3、25）＝（X＋22）（。28）．对于一些非二次三项式的多项式,通过适当的换元,可把它们转化为关于新变元的二次三项式,从而可用十字相乘法或配方法与公式法分解困式．例2分解因式：（x‘＋sx）‘－8（…     

用守恒法解化学题

所谓守恒法就是指选择化学变化过程中始终保持相等的两个量或化学反应前后保持不变的某微粒的数量作为解题依据的方法。守恒法主要有质量守恒法、电荷守恒法、电子守恒法、质子守恒法等。例１表示０．１mol／LNaHCO３溶液中有关微粒浓度关系的式子正确的是（）A．c（Na＋）＞c（HCO３－）＞c（CO３２－）＞c（H＋）＞c（OH－）B．c（Na＋）＋c（H＋）＝c（HCO３－）＋c（CO３２－）＋c（OH－）C．c（Na＋）＝c（CO３２－）＋c（HCO３－）＋c（H２CO３）＝０．１mol／LD．c（Na＋）＋c（H＋）＝c（HCO３－）＋c（OH－）＋…     

用配方法分解二次三项式

熟练掌握二次三项式的因式分解,有助于将来解决一元二次方程问题以及分式化简问题．对于二次三项式,十字相乘法是一种经常用到的分解方法．但对于系数较复杂的二次三项式,不容易用十字相乘法分解,一味地凑数分解往往费时费力．我们可以采用配方法来分解．配方法是以完全平方公式和平方差公式为基础进行恒等变形的分解方法：先将二次三项式配成一个完全平方式,然后再利用平方差公式分解,例如：（１）ｘ２－２ｘ－３＝（ｘ２－２ｘ＋１）－４＝（ｘ－１）２－４＝（ｘ－１＋２）（ｘ－１－２）＝（ｘ＋１）（ｘ－３）;（２）ｘ２（３）…     

细察特点 巧解方程

干什么事都有诀窍．解一元二次方程也是如此．一元二次方程有四种基本解法：直接开平方法、配方法、求根公式法、因式分解法．在解一元二次方程时,我们应当仔细观察方程的形式和系数特点,选择适当的方法,力求解题过程简洁、明快．例１解方程：3y（y－1）＝2－2y．特点方程两边都有因式（y－1）,宜用分解因式法．简解原方程就是移项并分解,得（y－1）（3y＋2）＝0．说明（1）本题多数同学只想到先整理成一般式,再分解困式,计算量就比较大．（2）有的同学将方程打（y－1）＝－2（y－i）两边同除以（y－1）,得打一一2,解得y＝－7二,…     

变形·转化·换元

学习了多项式的因式分解之后，同学们都知道，很多二次三项式都可用十字相乘法分解因式．例１分解因式：ｘ２－３ｘ－５４解因－９×６=－５４，且一９＋６=－３，所以原式=（ｘ－９）（ｘ＋６）．对于二次项系数为１、一次项系数为偶数的二次三项式，还可用配方法和公式法分解因式．例２分解因式：ｘ２－４ｘ－６２１解１用配方法．原式＝（ｘ２一４ｘ＋４）－６２５＝（ｘ－２）２－２５~２＝（ｘ－２＋２５）（ｘ－２－２５）＝（ｘ＋２３）（ｘ－２７）．解２用十字相乘法．因为－２７×２３＝－６２１，且－２７＋２３＝－４，所以原式…     

中考因式分解试题分析

纵观１９９７年全国各省市的中考试卷,关于因式分解的试题大致可分为如下３类：１．直接应用四种基本方法分解因式（１）分解因式：ｍａ＋ｂｍ＋ｍｃ＝．（广东）此题直接应用提公因式法分解因式．原式＝ｍ（ａ＋ｂ＋ｃ）．（２）分解因式：１６ａ２－９ｂ２＝．此题直接应用公式法分解因式．（天津）原式＝（４ａ＋３ｂ）（４ａ－３ｂ）．（３）分解因式：ｘ２＋２ｘ－１５＝．（河北）此题直接应用十字相乘法分解因式．原式＝（ｘ＋５）（ｘ－３）．此题也可用配方法分解因式．（４）用十字相乘法分解因式：５ｘ２＋６ｘｙ－８ｙ２＝．（…     

从二次三项式的因式分解谈起

同学们学习了用十字相乘法分解因式后都知道，许多二次三项式都可用十字相乘法分解因式．例1分解因式：。‘－5。一IO4·用因为一13X8—－104，且～13＋8一一5，所以原式一（X－13）（x＋8）．对于二次项系数为1、一次项系数为偶数的二次三项式，也可用配方法和公式法分解因式．例2分解因式：X’－2。‘－575·解1用配方法．原式一X’一ZX＋1－576二（－I）’一24。＝－1＋24）一l一24）一（J＋23）（J、一25）．俯2用十字相乘法．因为一25X23—－575，并且一25＋23一一2，所以原式一（X＋23）（x－％）．例3分解因式：x’－6X－616·…     

分组分解法的优化策略

分组分解法是因式分解的重要方法之一．分组的目的是通过恰当的分组,便于利用提公因式法、公式法或十字相乘法进行因式分解．正确的分组是前提,有预见性是正确分组的保证．下面介绍分组分解的６种优化策略,供同学们学习时参考．一、观系数,易分组例１分解因式：ａ３－２ａ２－３ａ＋６．分析此多项式中的一、二两项,三、四两项的系数之比都等于,因此可把它们分别分在同一组里,解决起来就易如反掌．解原式＝（ａ３－２ａ２）－（３ａ－６）＝２ａ２（ａ－２）－３（ａ－２）＝（ａ－２）（２ａ２－３）．同学们想上想,此题还有其他分…     

一道因式分解题的多种解法

分解因式：ｘ３－６ｘ２＋１１ｘ－６对于这样的三次四项式，既无公因式可提取，又不能用公式法、十字相乘法或分组分解法分解因式．因此，必须将它的某一项（常数项、一次项、二次项或三次项）拆成两项，然后用分组分解法分解因式．拆项分组的目的是使各组可分别用公式法、提公因式法或十字相乘法分解因式．一、拆常数项解１原式＝（ｘ３－１）－（６ｘ２－１１ｘ＋５）＝（ｘ－１）（ｘ２＋ｘ＋１）－（６ｘ－５）（ｘ－１）＝（ｘ－１）（ｘ２－５ｘ＋６）＝（ｘ－１）（ｘ－２）（ｘ－３）．解２原式＝（ｘ３－８）－（６ｘ２－１１ｘ－…     

因式分解方法的综合应用

将多项式分解因式,往往不能单一地使用某种方法,而是综合应用多种基本方法进行分解．解题的一般思考途径是：１．先看多项式是否有公因式可提取,若有,应先提取公因式;２．再看是否可用公式法或十字相乘法分解因式;３．若以上方法都不行,则应考虑用分组分解法分解因式：（１）是否能直接进行分组;（２）若不能直接分组,则应考虑拆项或添项分组,使得各组都有公因式可以提取,或可用公式法、十字相乘法进行分解．例１分解因式：（１）（ａ－ｂ）２－２ｃ（ｂ—ａ）＋ｃ２;（２）（３）ｘ３＋ｘ２ｙ－６ｘｙ２－ｘ＋２ｙ;（４）ａ３…     

卡思卡特城堡

It is worthy of noting that, whilst Crookston Castle witnessed the earlier and happier portion of Mary's variegated life,     

不同的吃喝玩乐

一、吃和喝吃苹果 eat an apple, 吃药 take medicine,吃糖 have some sweets,吃饭 have one's meals,吃馆子 dine out,吃惊 be surprised/     

漏洞百出的教育

Many college freshmen arrive woefully unprepared to do college work, and as disadvantaged populations continue to grow, the share of the American work force that has made it through college is expected to plummet. Many experts blame that educational failure not just on high schools but also on colleges. School & College, a special report by The Chronicle, looks at efforts to fix the system. What reforms would better prepare students for college? What should schools and colleges be doing differently? How should state and federal officials help?     

Western and Eastern culture differences in commercial field

The communication of people partially is the communication of cultures. Culture has a direct effect on international commercial activities in all aspects. Different conceptions about time, space, equality, law and the like, lead people to deal with things in different ways. So to know cultures of the counterpart is to facil-itate our enterprises so as to have a smooth and successful communication in commercial activity.     

只要努力,不要后悔

There are numbers of crossroads on our long and unpredictable life journey where we totally have no idea about which direction to choose. No matter what our decision is, we should not turn back, but face the music and go ahead instead. I am this kind of girl who always does try without regretting, one example is how I dealt with my love.     

浅谈移民问题

Migration occurs behind a variety of reasons and has a great effect on the whole world. People may migrate in order to improve their economic situation, or in order to escape civil strife, persecution, and environmental disasters. The impact of migration is complex, bringing both benefits anddisadvantages. This paper briefly talks about the causes of migration, the allocation of benefits, and the ways in which individual countries and the international community deal with this important subject.     

Sister Carrie, an Adherent of Desires

Sister Carrie is one of the most controversial characters in American literature.Thought as a "fallen woman" firstly,she was defined as a "new woman" by some critics later. However, by digging into the motivaton behind the whole process of Carrie's "success", the relationship between Carrie and her creator (the author), the social conditions of then American, it can be found that Carrie has never been free-standing on her thought and she has never found her real-sdf even after becoming a famous actress. In a society dominated by mass consumerism Carrie is only an adherent of her own desires. She also is a representative of all those country girls flooded into cities, a symbol and a sacrifice of the urbanization of America in a time countryside was overcome by cities.     

Improvement of one-cycle controller by use of proportional integral differential controller

1.IntroductionOne-cyclecontrolmethod,whichwasproposedaboutonedecadeago[1],hasbecomeanattractivemethodinspecialfieldssuchaspowerfactorcorrection[2-6],switchingamplifiers[7,8],etc.Themainideaofthiscontrollerisbasedonintegrationofdiodevoltageinone-cycleandforcesittobeexactlyequaltothereferencevalue.Themainadvantageofthiscontrollerisitsrealtimeabilitytorejectthevariationofinputvoltage[1].Despitethisgreatability,ithasnogoodperformancesinrejectingofloaddisturbanceandfollowingreferencecommands.Espec…     

风的曲线

Rosco and I wait for the fishermen to return.I sit at a wooden bench near the store at Mt.Baker Resort and watch the clouds change shape. Rosco has my belt around his neck and an eight foot tow chain hooked to a tree. Dogs must be on a leash. Ducks and rabbits are loose.